mühendislikdergisi Dicle Üniversitesi Mühendislik Fakültesi Mart 2014 bir model

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1 mühendislikdergisi Dicle Üniversitesi Mühendislik Fakültesi Cilt: 5, 1, 3-9 Mart 2014 Yatay eksenli rnin -teorik bir model Ondokuz Anahtar Kelimeler: teorik model. 69

2 M. C. enel, E. Koç Dynamic behaviour of horizontal axis wind turbines-a theoretical model Extended abstract Within renewable energy sources, wind energy is a natural, clean energy sources being observed that there is increasing use in recent years. Wind turbines are used to generate electricity energy from wind energy. Kinetic energy in wind turbine blades is converted into mechanical energy via power transmission systems, then, electrical energy is obtained from generator. They are classified as horizontal axis and vertical axis wind turbines according to the axis of rotation. In horizontal axis wind turbines, various power transmission mechanisms have been developed in order to obtain torque and power. These are direct drive, integrated, and conventional power transmission mechanisms. In a direct drive power transmission mechanism, torque and power are transmitted to the generator through a rotor. In an integrated power transmission mechanism, a gearbox and rotor are both used. In this study, conventional power transmission mechanism was used. Moreover, aerodynamic theories are used to determine the effect that wind has on the forces, torque, and power of blades of horizontal axis wind turbines. There are three main aerodynamic theories (one-dimensional lineer momentum theory, actuator disc momentum theory and blade element theory) related to wind turbine aerodynamics. Onedimensional momentum theory examines the force on the disc in the air flow tube. It is assumed that the disc consists of an infinite number of blades. The maximum power coefficient is limited to based on Betz' Law. Actuator disc momentum theory assumes that the disc consists of an infinite number of blades. Additionally, friction caused by the blade is neglected but the vortex effect of the flow is considered. Blade element theory is used to determine the forces and torque that affect on aerofoil. In present study, two different aerodynamic theories (actuator disc momentum theory, blade element theory) investigated in order to define the amount of torque affecting on the blades In this study, a new theoretical model was designed based on energy conversion for basic dynamic behaviour of the three blades-horizontal axis wind turbines. By this model, dynamic behaviour of wind turbine was assessed by evaluating design parameters, geometrical and physical sizes of the blade in accordance with torque equations. In addition, dimensional parameters were converted to dimensionless parameters. Thus, effect of many parameters such as wind speed, blade radius, mass of the blades, power coefficient, tip-speed ratio, axial induction factor and angular induction factor were analyzed. By this model, various dimensional torques could be estimated by changing m R G in the same nondimensional torque. Consequently, it was found that N G1 is very close to the nominal power of the referenced wind turbine (2 MW). Different dimensionless parameters so called as the coefficient of effectiveness (K t1, K t2 ) were defined in order to estimate the wind power transmitted to the generator and they were used for analyzing the wind turbines. It was determined that the dimensional parameters (wind speed (V), blade radius (R), the mass of the blades (m R )) and the non-dimensional parameters (tip- power coefficient ( )) directly affected the coefficient of effectiveness (K t ). In conclusion, K t1 and K t2 could be 0.38 and 0.37 respectively if the wind turbine parameters being as m R =19500 kg, R= 39.5 m, i=100. In addition, it was approximately determined that 38% of wind power was transmitted to the generator. When K t values were compared to values (when = ), the K t values were less than the values. Finally, this theoretical model presents a more realistic approach in terms of estimating the main parameters of wind turbine. Consequently, it is suggested that this theoretical study is used as a model for designing horizontal axis wind turbines. Keywords: Wind turbine, dynamic analysis, theoretical model. 70

is increasing use in recent years. Wind turbines are used to generate electricity energy from wind energy.

3 -teorik bir model G Enerji, ekonomik, sosyal ve kültürel enerjiye olan ba ini eyinin enerjisinin ). en abilir. Enerji Bu tip beraber ortalama 20- Yatay eksenli. Kanat utusu Anemometre Jeneratör (yaw) Kule merdiveni Kule k Temel durmayan kan (2008) Y. (2010), kanat eleman t - Huiying vd. (2010) 71

Enerji Bu tip beraber ortalama 20- Yatay eksenli.

4 M. C. enel, E. Koç P, C Q G G geom (R, m R diye yeni boyutsuz bir parametre Rüzgar türbini te torkutorka, K yatay eksenli bir modeli. V uç V R Kanat R i 1 z 1 z 2 i 2 kutusu A z 3 z 4 G, T G Jeneratör - P ), tork Q T ) ve uç - na na na. l = V / V = wr/ V (1) z V y uç r (Emniyetli, 2007). x R Aerofoil V Aerofoil R V uç 2 V ç - - Kanat a ekseniyle d r V Aerofoil referans ekseni 72

5 Yatay eksenli -teorik bir model - ( R C 2 3 P NR / N NR /(0.5 rpr V ) = = (2) olarak verilmektedir. aerodinamik olarak lineer momentum teorisine imitini(c pmaks Q ), itki k T Parametre Eksenel Tork ( V - V2 ) a = V ' W a = 2w C = C / l Q P C = C / R i T w Q = G G w = ar i>1 a Lineer momentum teorisine V 2 : Kanat hemen dn momentum teorisi - G R G Rüzgar türbini dinamik analiz-teorik model ni temel olarak; kanatlar, je momenti (I 1 ve I 4 momenti (I 2 ve I 3 momentine (I R ü I R T R T S Kanatlar Sistem 1 R I T S I 3 i I 2 d G kutusu T J Sistem 2 I 4 G TJ I G T G -komoment: mektedir. Kanat eleman teorisine dayanarak (T R1 ); (3) 73

45 Q ), itki k T Parametre Eksenel Tork ( V - V2 ) a = V ' W a = 2w C = C / l Q P C = C / R i T w Q = G G w = ar i>1 a Lineer momentum teorisine V 2 : Kanat hemen

6 M. C. enel, E. Koç 3 ), C Q tork (4) (5) moment ifadesi, (T R1 ) belirlenebilmektedir. omentum teorisine dayanarak R2 ); (6) boyutsuz moment; (7) (8) yutsuz momenttir. - tjmomenti: R (Nm), T S R 2 R ivmesi (rad/s 2 d (9) J momenti (Nm), T G G 2 ), I 2 G G 2 (10) d ) ve momenti (T S J (11) moment tek mile indirgenirse (T G ); (12) ; (13) R atalet momenti (kgm 2 ), I G atalet momenti (kgm 2 d d verimi; (14) nden atalet momentine (I R m R ' R 74

- tjmomenti: R (Nm), T S R 2 R ivmesi (rad/s 2 d (9) J momenti (Nm), T G G 2 ), I 2 G G 2 (10) d ) ve momenti

7 Yatay eksenli -teorik bir model biri (R/3) olarak kabul edilmektedir (Morren vd., 2006) atalet momenti (I R ); I e, G ve m R ( T G1 ); (15) (23) R R momenti (I ) ifadesi; (16) R, I G, I d ) ve moment R1, T R2 G ) bulunabilmektedir. (12)), T R1 ve I momenti (T G1 ); Q G d G ) G (m R G (I ) boyutsuz ifadeleri; (18) (19) (20) (21) (22) T, R1 T R1 (24) (25) momentidir. (12)), T R2 ve I (T G2 ); d G R hesaplanabilmektedir. narak T R2, I e, G ve m R ifadeleri momenti ( T G2 ); (27) T R2 (29) momentidir. 75

8 M. C. enel, E. Koç - ndan (T R1 bilmektedir. Bu durumda rüzgardan elde edilen güç (N R1 ); (30) olarak bulunabilmektedir. Bu ifadeden, R kanat P edilen gücü R1 ( ); (31) (32) moment (T R2 (N R2 ); (33) R2 esas ); (34) (35) - Jeneratör gücü (N G G ) G (36) G G (rad/s 2 edilmektedir. T R1 ve I (N G1 );,, G ve R ); (38) (39) (40) Jeneratör gücü (N G2 ), benzer G2 G ) ; T R1, I e, G ve R ( ); (42)

Bu ifadeden, R kanat P edilen gücü R1 ( ); (31) (32) moment (T R2 (N R2 ); (33) R2 esas ); (34)

9 Yatay eksenli -teorik bir model (43) (44) - G (K t ) s 2 V 3 ile N G1 (K t1 ); t1 ) R G d ve G 2 V 3 ile N G2 (K t2 ); V, m R G d G birimde olan parametreler yerine boyutsuz P - durumda R =19500 kg, G =1 rad/s 2 G1 =2.01 MW olarak m R G moment (N G1 ) tahmin edilebilmektedir. N G1 referans R =19500 kg) nominal =0.42, 77

yerine boyutsuz P - durumda R =19500 kg, G =1 rad/s 2 G1 =2.

10 M. C. enel, E. Koç N G1 1,8 1,6 1,4 1,2 1,0 0,8 0,6 0,4 0,2 0, =0.42 =0.44 =0.46 d =0.97 i=100 P boyutsuz = =0.174 R =19500 kg, R=39.5 m, V=15 G =1 rad/s 2 G2 boyutsuz momentte m R G edilebilmektedir. N G2 kaynakl ve NG2 G1 =N G2 =2.01 MW olarak tahmin g E1,2 ) N E1,2 g x N G1,2 E1,2 =1.97 MW N E E1,2 t t1 ve K t2 K t1 ) ve t1 P t1 t1 G ) 1 rad/s 2 G G t1 V=10 m/s, t1 =0.36 olarak K t1 0,42 0,40 0,38 0,36 0,34 0,32 0,30 0,28 0,26 0,24 0,22 0,20 0,18 =0,35 =0,40 =0,45 =0, V (m/s) =7 R=40 m i=100 G =1 rad/s 2 d =0.98 G =157 rad/s m R =19500 kg =1,2 kg/m 3 K t1 78

01 MW olarak tahmin g E1,2 ) N E1,2 g x N G1,2 E1,2 =1.97 MW N E E1,2 t t1 ve K t2 K t1 ) ve t1 P t1 t1 G ) 1 rad/s 2 G G t1 V=10 m/s, t1 =0.

11 Yatay eksenli -teorik bir model (m R t1 R kg t1 R t1 R =10500 kg, =0.37 iken; m R =19500 kg, m R R deki üzerine olan etkisi 2 2 R R R =19500 kg =0.25 iken; R=40 m, m R = R R ve m R üzerine olan etkisi m R ) kg 1 ve m R K t R 1=0.358, =0.352 iken; m R 1=0.352, = Referans (m R =19500 kg, R 1=0.38, 37- K t2 0,50 0,45 0,40 0,35 0,30 0,25 0,20 0,15 0,10 0,05 a=0.2 a=0.3 a=0.4 a=0.5 0,002 0,004 0,006 0,008 0,010 a' üzerine olan etkisi V=10 m/s R=40 m i=100 G =1 rad/s 2 d =0.98 G =157 rad/s m R =19500 kg =1.2 kg/m 3 Sonuçlar Teorik model ; g - boyutsuz jene 79

25 iken; R=40 m, m R =19500 2 2 R R ve m R üzerine olan etkisi m R ) 15000-19500 kg 1 ve m R K t R 1=0.358, =0.352 iken; m R 1=0.352, =0.344.

12 M. C. enel, E. Koç m i temel R =19500 kg, R=39.5 m, 1=0.38, =0.37 olarak t P ( = ); K t P t model olarak tavsiye edilmektedir. Semboller i d : : Hava (kg m -3 ) N J : T J : Jenera N G : T G : Jeneratör momenti (Nm) g : Jeneratör verimi I G 2 ) R : T R : T S : Kanatlardan : s -1 ) R : al ivmesi (rad s -2 ) V 2-1 ) I R 2 ) m R : V -1 ) N R : I : 2 ) N : V : s -1 ) N E ) K t : : Uç- G : Yükses -1 ) G : Yüksek rad s -2 ) nolu proje ile destek-. Kaynaklar Gazi - Dergisi, 23, 1, Yüksek Lisans Tezi Gregg, J. R., Trendrup ve J. J., Treuren, K.W.V., (2010). Developing a wind turbine design procedure with experimental vertification, 2010 ECTroceedings ASME Early Career Technical Conference, Tulsa. Huiying, C., Datong, Q. M. Z., Haitao, D., Yonggang, D. ve Wei, L., (2009). Research on evaluating of wind turbine drive train systems, Association of the Electricity Supply Industry of East Asia and Western Pacific CEO. Anadolu Enerji Sempozyumu, 610- Morren, J., Pierik, J. ve Haan, S. W. H., (2006). Inertial response of variable speed wind turbines, Electric Power Systems Research, 76, (2006). nerjisi urumu ve geklentiler, Atatürk Üniversitesi Ziraat Fak, 37, 2, (2012). iletim -dinamik d Fen Bilimun. ve (2013). t dinamik d analizi-teorik boyutsuz bir model, 2. Anadolu Enerji Sempozyumu, , 80

: V -1 ) N R : I : 2 ) N : V : s -1 ) N E ) K t : : Uç- G : Yükses -1 ) G : Yüksek rad s -2 ) nolu proje ile destek-. Kaynaklar Gazi - Dergisi, 23, 1, 41-47. Yüksek Lisans Tezi Gregg, J. R., Trendrup ve J.

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