mühendislikdergisi dergisi Dicle Üniversitesi Mühendislik Fakültesi Cilt: 5, 1, 3-9 Mart 014 Anin incelenmesi *, Fatih PEKER Mustafa Kemal Makine,3100, Özet gibi enerji kaynaklardan daha ucuz bir duruma rassal bir enerjisi potansiyeli istatistiksel olarak - - için (LSM Hata Kareleri olarak Antakya stiksel Anahtar Kelimeler: Antakya, Weibull - Log- *. ckarakus@mku.edu.tr; Tel: (36) 613 56 00 (4401) 13
. Mert, C. Investigation of wind characteristics for Antioch Extended abstract Rapidly increased the environmental pollution, global population and exhausted reserves of consuetudinary resources have become matters of social and economic concern to individuals and scientists since the '70s. With the rising costs of traditional energy resources, alternative renewable sources of energy are playing more important role. Actually, there is the many types of renewable energy resources such as hydro, solar, wind, biomass, geothermal, wave and tide energy. Among of them, the wind energy is maybe the cleanest, inexhaustible and popular source of energy. But wind energy has several disadvantages and one of them is that winds are inherently random. Wind power prediction processes give the information of how much wind power can be expected at which point of time in the determined time interval. However, these processes required the short and long-term wind characteristics and other measurements at a given location. In this respect, obtained wind speed, direction, humidity, pressure values and surface roughness information can provide fundamental and valuable information for the assessment of wind power energy availability and give knowledge for economic viability of a wind energy conversion system and also wind farm design. Turkey has important wind energy potential in the Akdeniz region, especially coasts of southern Anatolia. In this study, wind energy potential was statistically analyzed based on the data that are measured wind speed on a daily basis. Wind data obtained from the Directorate of Hatay Meteorological Station located Antioch which is central town of Hatay in southern Turkey, near the border with Syria in years between 00 and 009. A precise determination of probability distribution for wind speed data is the most important issue in statistically evaluating wind speed energy potential of a region. In generally, wind speed distribution have generally modeled by the 3-parameter Generalized Gamma, -parameter Gamma, inverse Gaussian, -parameter Lognormal, 3-parameter Beta, singly truncated from below Normal, distributions derived from the Maximum Entropy Principle, and conventional or bimodal (two component mixture) Weibull distribution functions etc.. But the wind energy potential of Antioch was investigated by Weibull Distribution that is popular. on the modeling of wind speed and Log-normal distribution function which is previously untested in Antioch. In the estimation of parameters of Weibull and log-normal distribution, the Maximum Likelihood Estimation (ML) and the Least Square Method (LSM) were used as the parameter estimation technique. The value of the Weibull shape parameter c is between.71 and 3.07 m/s, while the scale parameter k varies between 1.96 and.09 for ML method. When the LSM method is used, c is calculated between.61 and.96 m/s, while the scale parameter k varies between.34 and.53. If ML method use, the yearly values of Log-normal and 0.57. The lowest value of the Log-normal location parame-lsm) and found in the year 009, while the highest values were 0.84 (ML) and 0.86 (LSM), which occurred in the year 004. There are various tests used for evaluating the accuracy of the forecasted wind distributions obtained from various statistical functions. Both methods were evaluated by using error analysis that Average Square Root Sum of the Squares Error (RMSE). The highest root mean square error (RMSE) value was found as 0.00014 for the Lognormal distribution function by the ML method. The lowest RMSE value was calculated as 0.0164 by LSM method. Additionally these values were calculated 0.01081(ML) and 0.01458(LSM) for obtained using Log-normal distribution function are %98 in both methods, while the value is %99 for the Weibull distribution. The Weibull and Lognormal approximations of the actual probability distributions of wind speed for the whole year have close results. However, the best performance has been demonstrated by Weibull distribution with the ML method. The analysis results also showed that the maximum monthly wind speed occurs in the summer months while the months of winter have the lowest mean wind speed. The Weibull distribution provided better power density estimations in all months than the Log-normal distribution. As a result of this research when the wind turbines have low cut-in speed, were preferred, wind energy potential of Antakya was statistically found to be encouraging for production of electrical energy. Keywords: Antioch, Weibull Log-normal distribution, Least square method, Maximum likelihood estimation, Wind energy. 14
fere olan etmemesi, ekonomik dengelerden etkilenmesi ener -ge nerjisinden yararlanmak fikrini desteklemektedir. amda 138.5 Tureb, 01). zere, 00 009 Rüzgar enerjisi Ener geleneksel arz- kaynaklanan dalgalanmalardan etkilenmeyen, Birincisi, A hacmi (A.V.t) ve iler ½. ). Burada hava 3 P = E / t = A. 3 (1) ti ile. A r olarak Weibull, Rayleigh, Log-normal, Beta, Logistic, (Sen ve Sahin, 1997; Hepbasli vd., 001; Ozgener ve Hepbasli, 00; ise nispeten alara 15
. Mert, C. (004) rü (Sahin vd., 005). Bu meteoroloji istasyonundan elde edilen saatlik Weibull ve potansiyeli yine iki parametreli Weibull - (Eskin vd., 008). d, Weibull, Rayleigh, Gamma, ve Log- un -Bursa, Belen- (Ulgen ve Hepbasl vd., 007; Ucar ve Balo, 009; Sahin ve Bilgili, 009). Log- -normal Materyal metot An karakteristikleri o K; 36.1513 o D) 00- verileri yerden fiziki konumu ve Meteoroloji istasyonunun harita ( Openstreetmap, 01 ) - verilmektedir. 16
. Mert, C. filleri 17
. Mert, C. - -.1 m/s -.1- Weibull ve Log- (Maksimum) Olabilirlik Tahmini (ML) ile En belirleme Weibull ve Log- k1 k V V / c f k w( V ) e () c c - kuzey / kuzey- / - Metot Herha ve -009 lirlemek f w (V), V F w ( V) V / c 1 exp k (3) c ve k c ve k parametrelerinin tahmin edilmesi ile birlikte ise; 1 V Weibull c 1 (4) k. Burada, V Weibull ) ise Gamma fonksiyonunu ifade eder. Gamma fonksiyonunun genel ifadesi ise E verilebilir. 18
x t1 ( t) e x dx (5) 0 c ve k P w 3 1 c 3 (1 ) (6) k ile hesaplanabilir. Bu 3 ) olup hesaplamalarda 1.5 kg /m 3 kabul a Log- 5). Log- fonksiyonu, (lnv ) 1 Lognormal( x) e f (7) V eklinde verilmektedir. Burada, yer parametresi ve V Log normal e ( ) (8) ( )3 1 P L e (9) olarak ifade edilmektedir. Hata analizi Bunlardan birincisi R be R n ( yi xi ) i1 1 (10) n ( y y) i1 i olup; n RMSE ( 1 ( y i x i ) ) 0.5 (11) i1 Burada r Weibull ve Log-normal (. merkezde yer alan Meteoroloji Genel yerden k - leri ile tahmin edilen Weibull ve Log-normal 19
. Mert, C. için En Küçük Kareler (LSM) Tablo 1 de görülmektedir. c ( ölçek m/s en fazla 3.03 m/s k nin ise en da ektedir. - ) nin (yer-konum da mektedir her iki parametre kestiri- Tablo 1. -releri Parametre - 00 003 004 005 006 007 008 009 Weibull ML c.90 3.03 3.07 3.05 3.07.88.85.71 k.09.09.1 1.96 1.96 1.99.03.03.57.68.7.70.7.56.53.40 18.98 1.6.16 3.5 4.04 19.6 18.6 16.0 Std. Sapma 1.9 1.35 1.35 1.44 1.45 1.34 1.31 1.4 Weibull LSM c.79.9.96.93.95.77.76.61 k.53.47.53.34.8.46.34.40.47.59.63.59.6.45.44.3 14.46 16.99 17.38 17.7 18.64 14.46 14.78 1.3 Std. Sapma 1.05 1.1 1.11 1.18 1. 1.07 1.11 1.03 Log-normal ML 0.53 0.54 0.55 0.58 0.59 0.55 0.57 0.55 0.80 0.84 0.84 0.83 0.83 0.79 0.77 0.7.56.69.70.70.73.55.54.40 10.9 11.86 1.09 1.09 1.48 10.1 9.99 8.51 Std. Sapma 1.47 1.57 1.37 1.69 1.76 1.50 1.56 1.44 Log-normal LSM 0.5 0.53 0.5 0.56 0.57 0.54 0.56 0.55 0.80 0.84 0.86 0.83 0.83 0.78 0.77 0.7 Ort. H.55.67.70.68.71.53.5.39 10.10 11.64 1.07 11.83 1.16 9.97 9.79 8.35 Std. Sapma 1.43 1.5 1.51 1.64 1.69 1.47 1.5 1.41 Tablo. Weibull ML Weibull LSM Log-normal ML Log-normal LSM / m ) ) ) ) ) 00 10. 10.35161371 9.5413 10.944 10.1046818 003 11.6 11.83708804 10.6783 11.8593 11.64048793 004 11.9 1.9300053 11.1100 1.0853 1.077355 005 11.7 1.06615488 10.6808 1.0947 11.895469 006 11.7 1.3071193 10.9775 1.4760 1.15685154 007 9.9 10.37334 9.0590 10.1156 9.969065708 008 9.4 9.8784765 8.9148 9.9889 9.793559843 009 8.0 8.501113978 7.618 8.515 8.34900183 0
00- %99 ( Weibull ML ) en az ise %98 ( Log- en az 0.01081 ( Weibull ML ) en fazla 0.00014 ( Log-normal ML) Tablo 3. 00- Fonk. WEIBULL LOG-NORMAL METOD ML LSM ML LSM R 99% 99% 98% 98% RMSE 0.01081 0.01458 0.00014 0.0164 00- lar fonksiyonu ve parametre tahmini - neticesinde, parametre tahmin tekniklerinden ML- Log- -normal - Zeminden 10 m m/s ile 4.6 m/s ve 1.4 m/s potansiyeli olarak kuzey- - - de bu yap mekan Semboller A : Alan (m ) c (ms -1 ) F W (V) : Weibull birik f W (v) f Log-normal (V) : Log- : Gamma fonksiyonu K N P W (Wm - ) P L : Log-normal. Wm - ) P(V) (W) m -3 ) : Standart sapma (ms -1 ) V (ms -1 ) y x : Weibull-Log- hesaplanan ML : Maks. Olabilirlik Tahm. (EYO) LSM R² RMSE : Karekökü 1
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